Chelsea are believed to have increased their offer for the France winger, who has made it clear he wants to join the London club and claims he has already spoken to their manager Jose Mourinho.
Officials of the two clubs are now expected to meet in an attempt to conclude negotiations.
"A meeting between the directors of the two clubs will take place before the end of the week," a member of the Lyon board told L'Equipe.
Malouda, who Lyon value at £17million, left Les Gones' pre-season training camp midway through training on Wednesday.
Ligue 1's player of the year was driven away by a Lyon staff member from the Alpine ski resort of Tignes where Lyon are preparing for their bid to win a seventh consecutive Ligue 1 title.
Malouda, 27, was a key member of France's World Cup squad in Germany last year.
If he does complete a move to Stamford Bridge, he will link up once again with current Blues stars Didier Drogba and Michael Essien.
Malouda played with Drogba at Guingamp and Essien at Lyon.